Bulletin of Computational Applied Mathematics

19

Authors: Esmail Hesameddini, Mehdi Shahbazi

In this paper, a reliable algorithm for solving the nonlinear Hammerstein integral equation arising from chemical phenomenon is presented. The conductor-like screening model for real solvents (COSMO-RS) integral equation will be solved by the shifted Legendre collocation method. This method approximates the unknown function with Legendre polynomials. The merits of this algorithm lie in the fact that, on the one hand, the problem will be reduced to a nonlinear system of algebraic equations. On the other hand, we show that the efficiency and accuracy of the shifted Legendre collocation method for solving these equations are remarkable. Also, this method is using a simple computational manner and its error analysis will be discussed by illustrating some theorems. Finally, two numerical experiments are given to confirm the superiority and efficiency of presented method with respect to some other well-known methods such as the Bernstein collocation method, Haar wavelet method and Sinc collocation method.

23

Authors: Bruno H. Cervelin, Dante Conti, Denise T. Detsch, Maria A. Diniz-Ehrhardt, José Mario Martínez

Intensive broiler production requires of accurate control systems aimed to maintain ideal conditions inside the facilities. The achievement of an appropriate environment guarantees good performance and sustainability of the production. Control and monitoring of temperature is a key factor during the production cycle. In countries with tropical and subtropical climate, such as Brazil, high values of temperatures can affect negatively the broiler production. Based on a temperature control model developed by the authors, this research is focused on the determination and fitting of the intrinsic parameters of the model. Consecutive executions of the model and changes in the facilities suggest adapting parameters constantly under the perspective of real-time systems. Four strategies of derivative-free optimization were applied to adjust the parameters of the model. Experiments were conducted with data collected from a pilot farm in South-eastern Brazil. Results demonstrated that the process of updating parameters needs to be implemented on the temperature control model. BOBYQA method resulted to be the best strategy to be taken into consideration for the improvement of the system.

24

Authors: Debora Cores, Johanna Figueroa

The well-known Conjugate Gradient (CG) method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG) method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.